FEAT: initial changes

simulation/t01/.python-version

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+3.11

simulation/t01/README.md

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+- Para el 3 ordenarlo de menor a mayor
+    - Sea una m.a. de 10 elementos, entonces $F_n(x)$ 
+- Para el 3, después de simular la uniforme, evaluar en la función de distribución empírica obtenida previamente,
+    - Recordando que $F^{-1}(U)\sim F$ con $U\sim U(0,1)$

simulation/t01/data.py

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+#!/usr/bin/env python
+
+from yfinance import Ticker
+
+def get_data(tick:str = "^GSPC", years:int = 2, data_path:str = "data/"):
+    sp500 = Ticker(tick).history(period = f"{years}y")
+    print(sp500.describe())
+    sp500.to_csv(data_path + "sp500.csv", encoding='utf-8')
+
+def main():
+    get_data()

simulation/t01/gcl.py

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+#!/usr/bin/env python
+# from plotnine import *
+from math import gcd
+
+def gcl(x_n:int , a: int, c:int, m:int)->int:
+    return (a * x_n + c ) % m
+
+def normalize(vals:list[int])->list[float]:
+    max_val = max(vals)
+    return [v/max_val for v in vals]
+
+def is_prime(n:int)-> bool: 
+    for i in range(2, n): #for every value between 1 and n
+        if n % i == 0: #check if i divides n
+            return False #if this is true, n is not prime
+    return True if n > 1 else False #values less than 2 are not prime.
+
+def prim_root(m:int) -> list[int]:
+    required_set = { n for n in range(1, m) if gcd(n, m) }
+    return [ g for g in range(1,m) if required_set == { pow(g, powers, m) for powers in range(1, m) } ]
+
+def main():
+    # print(len(prim_root(3259)))
+    print(len(prim_root(3229)))
+    print(len(prim_root(3221)))
+    print(len(prim_root(3217)))
+
+if __name__ == "__main__":
+    main()

simulation/t01/main.py

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+#!/usr/bin/env python
+from gcl import gcl, prim_root, is_prime
+from plotnine import (
+    aes, ggplot, labs,
+    geom_histogram, geom_point
+)
+from numpy import var, average
+
+def plot_unif(y: list[float], media_path: str = "media/") -> None:
+    h = (
+        ggplot(aes(x = y))
+        + geom_histogram(bins = 25)
+        + labs(title = "Histograma de gcl")
+    )
+    d = (
+        ggplot(aes(x = range(0, len(y)), y = y))
+        + geom_point()
+        + labs(title = "Diagrama de dispersión de gcl")
+    )
+    d.save(media_path + "dispersion.png")
+    h.save(media_path + "histogram.png")
+    d.show()
+    h.show()
+    return y
+
+def print_ej1(n:int = 3259, n_sims: int = 1000):
+    q_is_prime = is_prime(n) 
+    yes_or_no = "sí" if q_is_prime else "no"
+    primitive_roots = prim_root(n)
+    print(f"Veamos que {n} {yes_or_no} es número primo")
+    print(f"Veamos que {n} tiene a {min(primitive_roots)} como su primera raíz primitiva")
+    if q_is_prime:
+        print("Un generador congruencial de periodo maximal es:")
+        print("x_{n+1}=" + str(min(primitive_roots)) + "x_n")
+        print("Con x_0 = 2")
+        print(f"Simulando {n_sims} con gcl")
+        sims = [ 2 ]
+        for _ in range(n_sims):
+            sims.append(gcl(sims[-1], min(primitive_roots), 0, n))
+        print("Medidas de tendencia central de la simulación")
+        print(f"Media: {average(sims)}")
+        print(f"varianza: {var(sims)}")
+        plot_unif(sims)
+
+def main():
+    print_ej1()
+
+
+if __name__ == "__main__":
+    main()

simulation/t01/pyproject.toml

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+[project]
+name = "t01"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+requires-python = ">=3.11"
+dependencies = [
+    "plotnine>=0.15.3",
+    "scipy>=1.17.1",
+    "yfinance>=1.2.0",
+]